The modal expansion of Kempner sums

Abstract

This is a continuation of the author's earlier paper Block-count constrained harmonic sums: spectral expansion and block-directed Euler--Maclaurin. We presented in that reference the modal expansion of block-Irwin sums $I(b,w,k)$ for $k\ge 1$. The case $k=0$ was fully developed when $w$ is a single digit, but it was presented only as a very short result summary for $w$ a multi-digit block. Although the framework is already completely exposed in the earlier paper, the case $k=0$ requires adding a separate, dedicated discussion, which is provided here.

29 pages, direct continuation of arXiv:2609.17045